We propose a simple mixtures estimator for recovering the joint distribution of parameter heterogeneity in economic models, such as the random coefficients logit. The estimator is based on linear regression subject to linear inequality constraints, and is robust, easy to program, and computationally attractive compared to alternative estimators for random coefficient models. For complex structural models, one does not need to nest a solution to the economic model during optimization. We present a Monte Carlo study and an empirical application to dynamic programming discrete choice with a serially correlated unobserved state variable.

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Thanks to research assistance from Chenchuan Li. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

The random coefficients, multinomial choice logit model has been widely used in empirical choice analysis for the last 30 years. We are the first to prove that the distribution of random coefficients in this model is nonparametrically identified. Our approach exploits the structure of the logit model, and so requires no monotonicity assumptions and requires variation in product characteristics within only an infinitesimally small open set. Our identification argument is constructive and may be applied to other choice models with random coefficients.