一种通用的需求反演方法
A General Method for Demand Inversion
摘要：
本文描述了一种数值方法来解决平均产品质量，相当于实际的市场份额的离散选择模型预测的市场份额。该方法涵盖了一般类型的离散选择模型，包括Berry和Pakes（2007）的纯特征模型和Berry等人的随机系数logit模型。（1995年）（以下简称BLP）。该方法将原市场份额反演问题转化为一个无约束凸极小化问题，使得任何凸规划算法都可用于求解该反演问题。此外，这样的结果也意味着反演需求模型的计算复杂性应该不超过凸规划问题。在仿真例子中，我表明该方法优于BLP中的压缩映射算法。我还发现，该方法在市场份额接近零的纯特征模型中仍然具有鲁棒性。
英文摘要：
This paper describes a numerical method to solve for mean product qualities which equates the real market share to the market share predicted by a discrete choice model. The method covers a general class of discrete choice model, including the pure characteristics model in Berry and Pakes(2007) and the random coefficient logit model in Berry et al.(1995) (hereafter BLP). The method transforms the original market share inversion problem to an unconstrained convex minimization problem, so that any convex programming algorithm can be used to solve the inversion. Moreover, such results also imply that the computational complexity of inverting a demand model should be no more than that of a convex programming problem. In simulation examples, I show the method outperforms the contraction mapping algorithm in BLP. I also find the method remains robust in pure characteristics models with near-zero market shares.
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