Reliable estimation of random coefficient logit demand models

The differentiated demand model of Berry, Levinsohn and Pakes (1995) is widely used in empirical economic research. Previous literature has demonstrated numerical instabilities of the corresponding GMM estimator that give a wide range of parameter estimates and economic implications depending on technical details such as the choice of optimization algorithm, starting values, and convergence criteria. We show that these instabilities are mainly driven by numerical approximation errors of the moment function which is not analytically available. With accurate approximation, the estimator is well-behaved. We also discuss approaches to mitigate the computational burden of accurate approximation and provide code for download.