Obesity is increasing worldwide and in many countries, the problem is particularly serious among lower income groups. To fight obesity, front-of-pack nutritional warning labels are a prominent regulatory tool that have been implemented or are currently debated in many countries. Existing studies document that warning labels incentivize consumers to substitute away from unhealthy products. However, not much is known about equilibrium price changes in response to consumers’ utility for warning labels. Using household purchase data in the cereal category, this paper studies the adjustments of prices after the mandatory introduction of warning labels in Chile. The authors develop a model which shows that warning labels lead to higher prices of labeled cereals, as is also observed in data. In contrast, prices of unlabeled products tend to drop or at least increase less, incentivizing price sensitive consumers to remain in the category. The authors decompose post-labeling market share adjustments into a pure label effect that fixes prices at initial levels after regulation and a total effect that accounts for price re-optimizations. Their findings point to self-enforcing effects of a warning label regulation as the price adjustments amplify the policy-maker’s goal of reducing unhealthy nutritional intake, especially because market forces incentivize low-income segments to choose healthier alternatives.
Models of consumer heterogeneity play a pivotal role in marketing and economics, specifically in random coefficient or mixed logit models for aggregate or individual data and in hierarchical Bayesian models of heterogeneity. In applications, the inferential target often pertains to a population beyond the sample of consumers providing the data. For example, optimal prices inferred from the model are expected to be optimal in the population and not just optimal in the observed, finite sample. The population model, random coefficients distribution, or heterogeneity distribution is the natural and correct basis for generalizations from the observed sample to the market. However, in many if not most applications standard heterogeneity models such as the multivariate normal, or its finite mixture generalization lack economic rationality because they support regions of the parameter space that contradict basic economic arguments. For example, such population distributions support positive price coefficients or preferences against fuel-efficiency in cars. Likely as a consequence, it is common practice in applied research to rely on the collection of individual level mean estimates of consumers as a representation of population preferences that often substantially reduce the support for parameters in violation of economic expectations. To overcome the choice between relying on a mis-specified heterogeneity distribution and the collection of individual level means that fail to measure heterogeneity consistently, we develop an approach that facilitates the formulation of more economically faithful heterogeneity distributions based on prior constraints. In the common situation where the heterogeneity distribution comprises both constrained and unconstrained coefficients (e.g., brand and price coefficients), the choice of subjective prior parameters is an unresolved challenge. As a solution to this problem, we propose a marginal-conditional decomposition that avoids the conflict between wanting to be more informative about constrained parameters and only weakly informative about unconstrained parameters. We show how to efficiently sample from the implied posterior and illustrate the merits of our prior as well as the drawbacks of relying on
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