40 Pages Posted: 23 Jan 2023
Date Written: January 20, 2023
Distributions of preferences and other economic primitives are often key inputs in market-level counterfactual analyses. In empirical work, these distributions must be inferred from finite amounts of data where measures of statistical fit often favor simple — yet ad-hoc — parametric assumptions. In this paper, we investigate ways of imbuing preference distributions with healthy doses of economic rationality through sign and order constraints. Such constraints naturally arise whenever product attributes such as quality or price can be vertically ordered a priori. We illustrate the merits and the disadvantages of imposing such constraints using (i) truncated normal and (ii) log-normal distributions. We then develop a model that enables the analyst to flexibly structure random coefficient distributions according to basic economic arguments using a combination of log-normal, truncated normal, and unconstrained distributions. We develop feasible Bayesian inference for this model based on MCMC, and illustrate that the proposed model improves the accuracy of counterfactual price predictions after the mandatory ban of cage eggs using German household scanner panel data.
Keywords: Constrained Hierarchical Prior, Discrete Choice, Bayesian Inference, Counterfactual Simulation
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