Improving the performance of random coefficients demand models: The role of optimal instruments

We shed new light on the performance of Berry, Levinsohn and Pakes’ (1995) GMM estimator of the aggregate random coefficient logit model. Based on an extensive Monte Carlo study, we show that the use of Chamberlain’s (1987) optimal instruments overcomes many problems that have recently been documented with standard, non-optimal instruments. Optimal instruments reduce small sample bias, but they prove even more powerful in increasing the estimator’s efficiency and stability. We consider a wide variety of data-generating processes and an empirical application to the automobile market. We also consider the gains of other recent methodological advances when combined with optimal instruments.