BLP模型中的条件矩估计与推断
Conditional-Moment Estimation and Inference in the BLP Model
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- University College London（伦敦大学学院）
- University of Melbourne（墨尔本大学）
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中文总结 AI 辅助
针对BLP模型，指出标准GMM因无条件矩限制可能导致识别失败，提出基于条件矩限制的两步估计器，达到半参数效率界且有限样本表现更优。
中文摘要 AI 辅助
Berry、Levinsohn和Pakes（1995）的随机系数需求模型通常通过广义矩方法（GMM）进行估计，该方法使用具有固定工具变量的无条件矩限制。然而，模型的识别依赖于条件矩限制。这两者并不等价：无条件限制可能允许额外的参数值。我们构造了一个反例，在该反例中，模型通过条件限制得以识别，但标准GMM即使使用最优工具也无法识别。直接基于识别限制，我们提出了一种两步估计器，遵循Ai和Chen（2003）的方法，首先非参数地估计相关的条件期望，然后通过条件方差加权的最小距离准则选择结构参数；标准GMM作为对有限个工具进行线性投影的特例被恢复。我们建立了所提出估计器的根号T渐近正态性，并为第一阶段的内核和级数实现发展了理论。这两种实现共享一个共同的极限分布，达到半参数效率界。模拟证据说明了识别差距的后果，并证明所提出的估计器在有限样本中优于标准GMM。
英文摘要
The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.
