Efficient Estimation of Random Coefficients Demand Models Using Product and Consumer Datasets

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Abstract

We propose a mixed-data likelihood estimator (MDLE) for a mixed logit demand system which makes use of product-level and consumer-level data while allowing for price endogeneity. The estimator is efficient compared to the GMM approach commonly used by applied researchers (e.g. Petrin, 2002; Berry, Levinsohn and Pakes, 2004). We show how to conduct inference on general functions of the model parameters, including elasticities. We further extend our approach to efficiently incorporate product-level exclusion restrictions commonly used to identify consumer heterogeneity when only product-level data is available (e.g., Berry, Levinsohn and Pakes, 1995; Nevo, 2001; Gandhi and Houde, 2020). These additional restrictions can improve precision when consumer-level data only weakly identifies consumer heterogeneity. We benchmark our likelihood-based estimator to the GMM approach with a Monte Carlo exercise and find superior performance in finite samples.