Discrete Choice Model Of Demand Research Articles

Exact algorithms for continuous pricing with advanced discrete choice demand models

Abstract We present a spatial Branch and Bound and spatial Branch and Benders Decomposition approach together with the Breakpoint Exact Algorithm (BEA) to tackle the uncapacitated choice-based pricing problem (CPP) where demand is captured by a discrete choice model (DCM) based on the random utility principle. We leverage problem characteristics to reformulate the state-of-the-art simulation-based formulation of the CPP as a mixed-integer linear program (MILP) into a non-convex quadratically constrained quadratic program (QCQP), and then into a non-convex QCQP with linear objective (QCQP-L). We solve this reformulation with an efficient spatial Branch and Bound procedure utilizing the McCormick envelope for relaxations, which are then solved using Benders decomposition. We further exploit utility breakpoints to develop the BEA, which scales polynomially in the number of customers and draws, providing a fast option for low numbers of prices. Our methods are evaluated against solving the MILP, QCQP, or QCQP-L with GUROBI on a mixed logit (ML) parking space operator case study. We outspeed the MILP by several orders of magnitude when optimizing one or two prices and reduce computational time drastically for larger numbers of prices. When comparing to algorithms tailored for the CPP with ML demand specifically, our approaches significantly outperform the state of the art. Our methodology suits all choice-based optimization problems with linear-in-price utilities, given any DCM.

Corporate Social Responsibility and Consumer Choice: Lessons from the Milk Boycott

We study the impact of a boycott on one of the largest Korean dairy producers, triggered by the exposure of the firm’s unethical management practices, on sales of its own and others. We find empirical evidence that the boycott had substantial and long-lasting consequences. First, consumer utility from the boycotted products decreased significantly, reflecting consumers’ strong willingness to take part in collective action. Second, our discrete choice demand model, which addresses both price endogeneity and product substitution, estimates that sales of the boycotted firm decreased by almost 8% or, equivalently, by 8.1 million liters during the 12-month postboycott period. Third, the boycotted firm’s sales and revenue decreases would have been more severe had the firm not cut prices after the boycott outbreak. Our findings emphasize top-level managers’ role in fostering an ethical organizational culture within the firm and taking proper and timely countermeasures to curb losses incurred by a boycott. This paper was accepted by Eric Anderson, marketing. Funding: This work was supported by the Asian Studies Center of Michigan State University [Dr. Delia Koo Faculty Endowment Award] and Sogang University [New Faculty Research Funding Grant 202310031.01]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01062 .

How Do Copayment Coupons Affect Branded Drug Prices and Quantities Purchased?

We estimate the causal effects of drug copayment coupons, which reduce consumer cost sharing for branded prescription drugs, on net-of-rebate price and quantities sold. We show that coupon introductions increase the quantity of drugs without generic substitutes sold by 23–25 percent for the commercial segment relative to Medicare Advantage, where coupons are banned. To quantify the resulting equilibrium price effects, we estimate a discrete choice model of demand for multiple sclerosis drugs and simulate a model of drug price negotiations. We estimate that net-of-rebate prices are 8 percent higher due to coupons being offered for most of these drugs. (JEL G22, I18, L65)

REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS

We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

A Random Coefficients Model of Seafood Demand: Implications for Consumer Preferences and Substitution Patterns

Discrete choice models of demand are growing in popularity for understanding markets for seafood, but have thus far been limited to applications using individual-level choice data. The random coefficients logit model is a discrete choice demand model designed for aggregate sales data and imparts a number of theoretical and empirical advantages. Instrumental variables account for price endogeneity, which can arise when there are unobserved product characteristics. Furthermore, correlated preferences can be accommodated in the random coefficients as well as through demographic interactions, which is especially important for seafood where product characteristics are primarily qualitative. We estimate this model for salmon fillets using four years of county-level seafood sales in California, and demonstrate the insights that can be drawn regarding consumer preferences and substitution patterns. Although the model is computationally burdensome, it offers considerable potential for further seafood demand analysis.

Cycling for Education? Heterogeneous Preferences for Academic Tracks at Secondary School

Using a unique data set from the Netherlands, I estimate a discrete choice demand model under congestion effects to recover preferences for secondary school tracks between parents with different socioeconomic status (SES) but equally proficient children. I find that highly educated parents are willing to let their offspring commute longer distances to attend tracks that grant direct admission to university. Valuation heterogeneity for such options explains more than half of the observed enrollment gap between students from different SES divides. These results suggest that low-SES children sort into academic tracks with lower economic prospects, even in schooling systems with negligible choice restrictions.

Omitted budget constraint bias in discrete-choice demand models

A large body of discrete-choice demand studies estimate a demand model in which the consumer’s budget constraint is not taken into account. We illustrate how incorrectly specifying the consideration set, when in fact the budget constraint binds for some products, may bias the demand estimates. We illustrate and quantify the nature of the bias in three ways: (i) in analytical examples; (ii) in field data commonly used in the literature and (iii) in a Monte Carlo study. We find that the price sensitivity can be substantially lower when correctly imposing the budget constraint, and own-price elasticities are typically overestimated although the direction of the own-price elasticity bias is in general ambiguous and depends on the income distribution.

Dynamic demand for differentiated products with fixed-effects unobserved heterogeneity

Summary This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumer-level panel data with few purchase events per consumer (i.e., short panel). Consumers are forward-looking and their preferences incorporate two sources of dynamics: last choice dependence due to habits and switching costs, and duration dependence due to inventory, depreciation, or learning. A key distinguishing feature of the model is that consumer unobserved heterogeneity has a Fixed Effects structure; that is, its probability distribution conditional on the initial values of endogenous state variables is unrestricted. I apply and extend recent results to establish the identification of all the structural parameters as long as the dataset includes four or more purchase events per household. The parameters can be estimated using a sufficient statistic—conditional maximum likelihood (CML) method. An attractive feature of CML in this model is that the sufficient statistic controls for the forward-looking value of the consumer’s decision problem, such that the method does not require solving dynamic programming problems or calculating expected present values.

Rational Inattention as an Empirical Framework for Discrete Choice and Consumer-Welfare Evaluation

The conventional discrete-choice model of demand assumes that consumers are fully informed about every available product alternative. This assumption is at odds with the large body of literature studying incomplete information and the role of the consumer's “evoked set” or “consideration set.” The author develops a novel empirical discrete-choice demand model derived from an underlying theory of consumers' rational inattention. The model distinguishes between factors that shift demand through the utility function, such as prices and product attributes, and factors that shift demand through the consumer's information “evaluation costs.” The author conducts an empirical case study of the laundry detergent category. Using a set of exclusion restrictions based on retail promotional instruments, specification tests select the rational inattention model over the conventional full-information discrete-choice model. Exploiting the launch of Tide Pods midway through the sample, the author demonstrates the role of evaluation costs for the measured value creation from a new product. A conventional discrete-choice model always assigns positive incremental consumer value from new products. However, the rational inattention model developed herein finds a decrease in overall consumer welfare from the new Tide Pods’ entry, with the increased friction in information associated with the larger choice set offsetting the potential gains from higher match value.

Decomposing the effect of advertising: What happens in the retail channel?

The diverging interests of manufacturers and retailers famously give rise to the double marginalization problem but have consequences far beyond pricing. Advertising is another marketing instrument that is under the control of the manufacturer but its ultimate effect on consumer demand also depends on retailers’ pricing decisions. We decompose the effect of advertising in the channel and highlight an additional route through which advertising affects sales, namely via the changes in the retail price that a strategic retailer makes in response to changes in demand following manufacturer advertising. The total demand effect of advertising thus comprises the direct effects of advertising on market shares, and the indirect effects coming through adjustments that the retailer makes to the in-store prices of all the brands in a given product category in response to the shifted demand due to advertising. We match advertising data for four different categories (both food and non-food) to store-level scanner panel data, which also include information on wholesale prices. Controlling for wholesale prices, we establish in a reduced-form model that the retailer reacts to manufacturer advertising by changing retail prices instead of simply imposing a constant markup on the wholesale price. To further explore the role of the strategic response of the retailer in a systematic fashion and quantify the effects derived in the decomposition, we estimate a discrete-choice model of demand and determine the magnitude of the direct and indirect effects. We find that the indirect effect of advertising through retailer prices is about half the size of the direct effect, and thus substantively affects advertising effectiveness.

Consumer Search and Prices in the Automobile Market

Abstract This article develops a discrete choice model of demand with optimal sequential consumer search. Consumers first choose a product to search; then, once they learn the utility they get from the searched product, they choose whether to buy it or to keep searching. We characterize the search problem as a standard discrete choice problem and propose a parametric search cost distribution that generates closed-form expressions for the probability of purchasing a product. We propose a method to estimate the model that supplements aggregate product data with individual-specific data which allows for the separate identification of search costs and preferences. We estimate the model using data from the automobile industry and find that search costs have non-trivial implications for elasticities and markups. We study the effects of exclusive dealing regulation and find that firms benefit at the expense of consumers, who face higher search costs and higher prices than would be the case if multi-brand dealerships were used.

Private Labels Strategy, Retail Profitability and Bargaining Power in the Fluid Milk Market

Abstract This paper studies the competition between private labels and the role of private labels in determining the bargaining outcomes between retailers and manufacturers as well as retailer profitability in the fluid milk market. We differentiate private labels from different retailers and develop a structural model of demand and a Nash-in-Nash vertical bargaining model of supply. Using 2004–2011 Nielsen Homescan data at monthly-county level, we estimated the average bargaining power of retailers and how various factors influence their bargaining power with a random-coefficient discrete choice model of demand. With the full bargaining model specification, this paper then conducts simulations to isolate the role of private label in bargaining and retailer profitability, comparing the effectiveness of alternative private label strategies. Results indicate private label milk from different retailers are close competitors and retailers have more bargaining power than manufacturers. Further, factors such as the manufacturer size, private label share, and their private label position can significantly affect retailers’ bargaining power. Moreover, the counterfactual analysis shows that lowering private label prices and other private label strategies such as private label program expansion and retailer advertising could not only increase their profitability but also allow retailers to benefit from the bargaining with manufacturers.

Identification and Estimation of Discrete Choice Demand Models When Observed and Unobserved Characteristics are Correlated

Identification and Estimation of Discrete Choice Demand Models When Observed and Unobserved Characteristics are Correlated

Price-based regulation of oligopolistic markets under discrete choice models of demand

We propose a framework to find optimal price-based policies to regulate markets characterized by oligopolistic competition and in which consumers make a discrete choice among a finite set of alternatives. The framework accommodates general discrete choice models available in the literature in order to capture heterogeneous consumer behavior. In our work, consumers are utility maximizers and are modeled according to random utility theory. Suppliers are modeled as profit maximizers, according to the traditional microeconomic treatment. Market competition is modeled as a non-cooperative game, for which an approximate equilibrium solution is sought. Finally, the regulator can affect the behavior of all other agents by giving subsidies or imposing taxes to consumers. In transport markets, economic instruments might target specific alternatives, to reduce externalities such as congestion or emissions, or specific segments of the population, to achieve social welfare objectives. In public policy, different agents have different individual or social objectives, possibly conflicting, which must be taken into account within a social welfare function. We present a mixed integer optimization model to find optimal policies subject to supplier profit maximization and consumer utility maximization constraints. Then, we propose a model-based heuristic approach based on the fixed-point iteration algorithm that finds an approximate equilibrium solution for the market. Numerical experiments on an intercity travel case study show how the regulator can optimize its decisions under different scenarios.

The geography of ridesharing: A case study on New York City

Despite the popularity of ridesharing, there is limited empirical evidence on how ridesharing activities differ across regions with different levels of accessibility and the implication for consumers. In this paper, we study the market for rides across New York City neighborhoods. We construct a novel data set that contains massive API queries on route-specific estimates of pricing, wait time, and travel time of Uber, Lyft, and the public transit. After linking this data with actual trip records of taxis, Uber, and Lyft, we document a strong pattern that ridesharing has a larger market share relative to taxis in neighborhoods with lower accessibility, defined either in terms of geographic distance to Midtown Manhattan or “economic distance” to job opportunities. Next, we estimate a discrete-choice model of demand for rides and interpret the geography of ridesharing through the lens of the model. We find that consumer surplus from ridesharing varies drastically across geography: passengers that are 5 to 15 miles (resp. more than 15 miles) from Midtown experience a 60% (resp. 19%) larger consumer surplus relative to passengers that are within 5 miles from Midtown. Over half of these gains comes from reduced wait time.

Preference or technology? Evidence from the automobile industry

Which comes first in reducing the Carbon Dioxide (CO2) emissions from the transportation sector: consumer preference or technological advancement? Using a series of discrete-choice demand models, we estimate the demand for automobiles in Japan. Our model explicitly allows consumer preferences for fuel economy to evolve over time, and the estimation results confirm the existence of such a change. We then simulate consumer behavior, enabling consumers in 2010 to choose automobiles from 2016, and vice versa. The results imply that both consumer preferences and technological advancement are important—without technological advancement and increases in consumers’ appreciation for fuel-efficient cars, CO2 emissions cannot be reduced.

Ethical management and consumer choice: Lessons from the milk boycott

We study the impact of a boycott on one of the largest Korean dairy producers, triggered by the exposure of the firm's unethical management practices, on its product sales and prices. We find empirical evidence that the boycott had substantial and long lasting consequences. First, consumer utility from the boycotted products decreased significantly, reflecting consumers' strong willingness to take part in the collective action. In addition, consumers with lower income or larger family size participated in the boycott more actively. Second, our discrete choice demand model, which addresses both heterogenous effects of the boycott and price endogeneity, estimates that sales of the two boycotted products decreased by 7.9 million liters in total during the 10-month post-boycott period, whereas sales of competing non-boycotted products increased by 3 million liters in the same period. Third, the decrease in sales and revenue was less severe for the product for which the boycotted firm sharply cut the price; our counterfactual analysis predicts that the firm's post-boycott revenue loss would have been higher by 75.8 percent had the price cut not been made. Our findings emphasize top-level managers' role in fostering an ethical organizational culture within the firm as well as taking proper and timely countermeasures to curb losses incurred by a boycott.

Estimating Complementarity With Large Choice Sets: An Application to Mergers

Standard discrete choice demand models assume that products are substitutes. Merger analyses based on these models may overstate consumer harm when producers of complementary products merge. Allowing for demand complementarity greatly complicates demand estimation, particularly when the number of choices is large. We introduce a straightforward Generalized Method of Moments estimator that identifies preferences allowing for (1) potential consumption complementarity, (2) price endogeneity and (3) large choice sets. Our estimator parsimoniously leverages information on consumer level bundle specific purchases and aggregate sales data. We apply this estimator to the chips and soda market and find a high degree of complementarity between these product groups. We show that a merger between PepsiCo/Frito-Lay and Dr. Pepper would increase soda prices by 30% less than suggested by a model that does not account for complementarity. Post-merger chip prices decrease. Overall, accounting for complementarity leads to positive welfare gains in some markets with large numbers of Frito-Lay varieties.

Demand Modeling in the Presence of Unobserved Lost Sales

We present an integrated optimization approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We employ a mixed-integer program (MIP) to jointly determine the prediction parameters associated with the customer arrival rate and their substitutive choices. This integrated approach enables us to recover proven, (near-) optimal parameter values with respect to the chosen loss-minimization (LM) objective function, thereby overcoming a limitation of prior multistart heuristic approaches that terminate without providing precise information on the solution quality. The imputations are done endogenously in the MIP by estimating optimal values for the probabilities of the unobserved choices being selected. Under mild assumptions, we prove that the approach is asymptotically consistent. For large LM instances, we derive a nonconvex-contvex alternating heuristic that can be used to obtain quick, near-optimal solutions. Partial information, user acceptance criteria, model selection, and regularization techniques can be incorporated to enhance practical efficacy. We test the LM model on simulated and real data and present results for a variety of demand-prediction scenarios: single-item, multi-item, time-varying arrival rate, large-scale instances, and a dual-layer estimation model extension that learns the unobserved market shares of competitors.This paper was accepted by Yinyu Ye, optimization.

Consumer search in the U.S. auto industry: The role of dealership visits

In many markets, consumers visit stores and physically inspect products before making purchase decisions. We view the inspection of a product at a retail location as a search for product fit. We quantify the cost and benefit from searching for product fit using a discrete choice model of demand with optimal sequential search. In these models, the benefit of searching is measured by the standard deviation of the product fit and has, heretofore, been fixed to one in estimation. We show that, with an exogenous search cost shifter, both the cost and benefit of searching can be separately estimated. Our empirical setting is the U.S. automotive market. We assemble a unique data set containing individual-level smartphone geolocation data that inform us about dealership visits. We also obtain information on new vehicle purchases from proprietary DMV registration data. Our exogenous cost shifter is the distance a consumer must travel to visit a dealership. Our results show that the benefit provided by dealerships to consumers is substantial. Within our empirical context, failure to estimate the standard deviation of the product fit leads to biased search cost and consumer surplus estimates and to inaccurate predictions regarding consumers’ number of searches and effects of at-home test drive programs.