Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation
研究了BLP估计器中嵌套不动点算法的数值问题，提出将估计转化为带均衡约束的数学规划，可避免数值错误并大幅提升计算速度，对静态和动态模型均有效。
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 objective 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 the Bellman 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.For static BLP, the constrained optimization approach can be as much as ten to forty times faster for large-dimensional problems with many markets.