Simulation Error and Numerical Instability in Estimating Random Coefficient Logit Demand Models

The nonlinear GMM-IV estimator of Berry, Levinsohn and Pakes (1995) can suffer from numerical instability resulting in a wide range of parameter estimates and economic implications. This has been reported to depend on technical details such as the choice of the optimization algorithm, starting values, and convergence criteria. We show that numerical approximation errors in the estimator's moment function are the main driver of this instability. With accurate approximation, the estimation approach is well-behaved. We provide a simple method to determine the required number of simulation draws.