## Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation (2008)

Citations: | 20 - 0 self |

### BibTeX

@TECHREPORT{Dubé08improvingthe,

author = {Jean-pierre Dubé and Jeremy T. Fox and Che-lin Su},

title = {Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation},

institution = {},

year = {2008}

}

### OpenURL

### Abstract

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