The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces consistent instrumental variables estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and potentially endogenous regressors (prices). The nested fixed-point algorithm typically used for estimation is computationally intensive, largely because a system of market share equations must be repeatedly numerically inverted. We provide numerical theory results that characterize the properties of typical nested fixed-point implementations. We use these results to discuss several problems with typical computational implementations and, in particular, cases which can lead to incorrect parameter estimates. As a solution, we introduce a new computational formulation of the estimator that recasts estimation as a mathematical program with equilibrium constraints (MPEC). In many instances, MPEC is faster than the nested fixed point approach. It also avoids the numerical issues associated with nested inner loops. Several Monte Carlo experiments support our numerical concerns about NFP and the advantages of MPEC. We also discuss estimating static BLP using maximum likelihood instead of GMM. Finally, we show that MPEC is particularly attractive for forward-looking demand models where

The US mobile phone service industry has dramatically consolidated over the last two decades. One justification for consolidation is that merged firms can provide consumers with larger coverage areas at lower costs. We estimate the willingness to pay for national coverage to evaluate this justification for past consolidation. As market level quantity data are not publicly available, we devise an econometric procedure that allows us to estimate the willingness to pay using market share ranks collected from the popular online retailer Amazon. Our semiparametric maximum score estimator controls for consumers ’ heterogeneous preferences for carriers, handsets and minutes of calling time. We find that national coverage is strongly valued by consumers, providing an efficiency justification for across-market mergers. The methods we propose can estimate demand for other products using data from online retailers where product ranks, but not quantities, are observed.

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discretechoice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical application to US automobile demand.