The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates
of consumer preferences from a discrete-choice demand model with random coefficients,
market-level demand shocks and endogenous prices. We derive numerical theory results
characterizing the properties of the nested fixed point algorithm used to evaluate the
ob jective function of BLP’s estimator. We discuss problems with typical implementations,
including cases that can lead to incorrect parameter estimates. As a solution, we recast
estimation as a mathematical program with equilibrium constraints, which can be faster
and which avoids the numerical issues associated with nested inner loops. The advantages
are even more pronounced for forward-looking demand models where Bellman’s equation
must also be solved repeatedly. Several Monte Carlo and real-data experiments support
our numerical concerns about the nested fixed point approach and the advantages of
constrained optimization.