SMU SOE Seminar Series (May 9, 2025): A Quasi-Bayes Approach to Nonparametric Demand Estimation with Economic Constraints

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ABSTRACT

This paper presents a quasi-Bayes approach to estimating nonparametric demand systems for differentiated products. We transform the GMM objective function developed by Compiani (2022) into a quasi-likelihood, specify priors that penalize violations of micro-founded economic constraints, and develop novel Bayesian inference procedures. We use simulations and retail scanner data from 12 consumer packaged goods categories to show that our quasi-Bayes approach improves both the accuracy of estimated elasticities and the validity of estimated demand functions. Together, our results demonstrate the value of (i) disciplining flexible nonparametric estimators with judicious economic constraints, and (ii) Bayesian methods for accommodating such constraints. Finally, we introduce a new Julia package (NPDemand.jl) that implements both GMM and quasi-Bayes approaches to estimation.

Keywords: Differentiated Products, Price Elasticities, Shape Constraints, Bernstein Polynomials, Nonparametric Instrumental Variables, Sequential Monte Carlo, Counterfactual Analysis.

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